# COMQ: A Backpropagation-Free Algorithm for Post-Training Quantization

arXiv: https://arxiv.org/abs/2403.07134 · HTML: https://mlsanity.com/paper/2403.07134/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 67 references that are in the map.
- First posted on arXiv 11 Mar 2024.

## Builds on (most cited first, 30 of 49)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Up or Down? Adaptive Rounding for Post-Training Quantization](https://mlsanity.com/paper/2004.10568/) (2020)
- [DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradients](https://mlsanity.com/paper/1606.06160/) (2016)
- [BRECQ: Pushing the Limit of Post-Training Quantization by Block Reconstruction](https://mlsanity.com/paper/2102.05426/) (2021)
- [PACT: Parameterized Clipping Activation for Quantized Neural Networks](https://mlsanity.com/paper/1805.06085/) (2018)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [Data-Free Quantization Through Weight Equalization and Bias Correction](https://mlsanity.com/paper/1906.04721/) (2019)
- [Optimal Brain Compression: A Framework for Accurate Post-Training Quantization and Pruning](https://mlsanity.com/paper/2208.11580/) (2022)
- [Post-Training Quantization for Vision Transformer](https://mlsanity.com/paper/2106.14156/) (2021)
- [ZeroQ: A Novel Zero Shot Quantization Framework](https://mlsanity.com/paper/2001.00281/) (2020)
- [Post-training Quantization on Diffusion Models](https://mlsanity.com/paper/2211.15736/) (2022)
- [Understanding Straight-Through Estimator in Training Activation Quantized Neural Nets](https://mlsanity.com/paper/1903.05662/) (2019)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)

## Built on by (most cited first, 12 of 12)

- [PTQ4DiT: Post-training Quantization for Diffusion Transformers](https://mlsanity.com/paper/2405.16005/) (2024)
- [MagR: Weight Magnitude Reduction for Enhancing Post-Training Quantization](https://mlsanity.com/paper/2406.00800/) (2024)
- [Model Quantization and Hardware Acceleration for Vision Transformers: A Comprehensive Survey](https://mlsanity.com/paper/2405.00314/) (2024)
- [FP4DiT: Towards Effective Floating Point Quantization for Diffusion Transformers](https://mlsanity.com/paper/2503.15465/) (2025)
- [CLoQ: Enhancing Fine-Tuning of Quantized LLMs via Calibrated LoRA Initialization](https://mlsanity.com/paper/2501.18475/) (2025)
- [Beacon: Post-Training Quantization with Integrated Grid Selection](https://mlsanity.com/paper/2508.20293/) (2025)
- [Optimal Post-Training Quantization Scales and Where to Find Them](https://mlsanity.com/paper/2606.10890/) (2026)
- [Eigen Neural Network: Unlocking Generalizable Vision with Eigenbasis](https://mlsanity.com/paper/2508.01219/) (2025)
- [Binary Quadratic Quantization: Beyond First-Order Quantization for Real-Valued Matrix Compression](https://mlsanity.com/paper/2510.18650/) (2025)
- [RPIQ: Residual-Projected Multi-Collaboration Closed-Loop and Single Instance Quantization for Visually Impaired Assistance](https://mlsanity.com/paper/2601.02888/) (2026)
- [Two-Stage Grid Optimization for Group-wise Quantization of LLMs](https://mlsanity.com/paper/2602.02126/) (2026)
- [Weight Group-wise Post-Training Quantization for Medical Foundation Model](https://mlsanity.com/paper/2604.07674/) (2026)

## Abstract (arXiv)

Post-training quantization (PTQ) has emerged as a practical approach to compress large neural networks, making them highly efficient for deployment. However, effectively reducing these models to their low-bit counterparts without compromising the original accuracy remains a key challenge. In this paper, we propose an innovative PTQ algorithm termed COMQ, which sequentially conducts coordinate-wise minimization of the layer-wise reconstruction errors. We consider the widely used integer quantization, where every quantized weight can be decomposed into a shared floating-point scalar and an integer bit-code. Within a fixed layer, COMQ treats all the scaling factor(s) and bit-codes as the variables of the reconstruction error. Every iteration improves this error along a single coordinate while keeping all other variables constant. COMQ is easy to use and requires no hyper-parameter tuning. It instead involves only dot products and rounding operations. We update these variables in a carefully designed greedy order, significantly enhancing the accuracy. COMQ achieves remarkable results in quantizing 4-bit Vision Transformers, with a negligible loss of less than 1% in Top-1 accuracy. In 4-bit INT quantization of convolutional neural networks, COMQ maintains near-lossless accuracy with a minimal drop of merely 0.3% in Top-1 accuracy.